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Circle - 1 - JEE MCQ


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30 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Circle - 1

Circle - 1 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Circle - 1 questions and answers have been prepared according to the JEE exam syllabus.The Circle - 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Circle - 1 below.
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Circle - 1 - Question 1


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Circle - 1 - Question 2


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Circle - 1 - Question 3


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Circle - 1 - Question 4

The possible radius of a circle whose centre is at the origin and which touches the circle x2 + y2 – 6x – 8y + 21 = 0, is

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Circle - 1 - Question 5


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Circle - 1 - Question 6


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Circle - 1 - Question 7

A circle passes through the points (- 1, 1) ,  (0, 6) and  (5, 5) . The point(s) on this circle, the tangent(s) at which is/are parallel to the straight line joining the origin to its centre is/are :

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Circle - 1 - Question 8


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Circle - 1 - Question 9

In a triangle ABC with fixed base BC, the vertex A moves such that cos C – cos B = cos2 A/2 . If a, b and c denote the lengths of sides of the triangle opposite to angles A, B and C, respectively, then which one of the following is correct?

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Circle - 1 - Question 10


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Circle - 1 - Question 11


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Circle - 1 - Question 12


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Circle - 1 - Question 13

The locus of the point of intersection of the tangent to the circle x2 + y2 = a2, which include an angle of 45° is the curve  (x2 + y2)2 = λa2 (x2 + y2 – a2). The value of λ is

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Circle - 1 - Question 14


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Circle - 1 - Question 15


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Circle - 1 - Question 16


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Circle - 1 - Question 17

The locus of the point of intersection of the tangent to the circle x2 + y2 = a2, which include an angle of 45° is the curve 

(x2 + y2)2 = λa2 (x2 + y2 – a2). The value of λ is

Detailed Solution for Circle - 1 - Question 17


Circle - 1 - Question 18


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Circle - 1 - Question 19


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Circle - 1 - Question 20


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Circle - 1 - Question 21

The possible radius of a circle whose centre is at the origin and which touches the circle x2 + y2 – 6x – 8y + 21 = 0, is

Detailed Solution for Circle - 1 - Question 21

Let r be the radius of required circle. Now, if two circles touches each other then distance between their centres =|r ± 2| = 5 (given)
∴    r = 3, 7
Note: Equation of circles are x2 + y2 = 9 or x2 + y2 = 49

Circle - 1 - Question 22


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Circle - 1 - Question 23


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Circle - 1 - Question 24


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Circle - 1 - Question 25

The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq. units. The equation of the circle is

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Circle - 1 - Question 26

The equation of the circle passing through (3, 6) and whose centre is (2, –1) is

Detailed Solution for Circle - 1 - Question 26

(x−2)2+(y+1)2 = r2

(3,6). lies on it

⇒ 1+49=r2

⇒ r2=50

⇒ x2+4−4x+y2+1+2y=50.

⇒ x2+y2−4x+2y−45=0

Circle - 1 - Question 27

y = √3x + c1 & y = √3x + c2 are two parallel tangents of a circle of radius 2 units, then |c1 – c2| is equal to

Detailed Solution for Circle - 1 - Question 27

For both lines to be parallel tangent the distance between both lines
should be equal to the diameter of the circle
⇒ 4 = |c1−c2|/(1+3)1/2
⇒∣c1−c2∣ = 8

Circle - 1 - Question 28

The area of an equilateral triangle inscribed in the circle x2 + y2 – 2x = 0 is

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Circle - 1 - Question 29

The gradient of the tangent line at the point (a cos a, a sin a) to the circle x2 + y2 = a2, is

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Circle - 1 - Question 30

The greatest distance of the point P(10, 7) from the circle x2 + y2 – 4x – 2y – 20 = 0 is

Detailed Solution for Circle - 1 - Question 30

Centre and radius of the given circle are C(2,1) and √4+1+20 = 5 respectively.
Now CP=√82+62=10. Hence greatest distance of point P from the given circle is =10+r=15

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